SOLUTION: Find the half-life of a certain radioactive substance which decays according to the formula 𝑦 = 100𝑒 −3𝑡 , where y is the amount present after t years?

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Find the half-life of a certain radioactive substance which decays according to the formula 𝑦 = 100𝑒 −3𝑡 , where y is the amount present after t years?       Log On


   

Question 1187783: Find the half-life of a certain radioactive substance which decays according to the
formula 𝑦 = 100𝑒
−3𝑡
, where y is the amount present after t years?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The notation needs to be done correctly.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Find the half-life of a certain radioactive substance which decays according to the formula 𝑦 = 100%2Ae%5E%28-3t%29,
where y is the amount present after t years?
~~~~~~~~~~~~~~~~~~ 

The initial mass is 100 units at t= 0.


At the half-life value of t,  the remaining mass is  100%2F2 = 50.


So we write the decay equation in  ekt-form


    50 = 100%2Ae%5E%28-3t%29

    50%2F100 = e%5E%28-3t%29

    0.5 = e%5E%28-3t%29


Take logarithm base "e"  (natural logarithm) of both sides


   ln(0.5) = -3t


Express "t" and calculate


    t = ln%280.5%29%2F%28-3%29 = 0.231049  years.    ANSWER


CHECK.  100%2Ae%5E%28-3%2A0.231049%29 = 100%2A2.71828%5E%28-3%2A0.231049%29 = use your calculator = 50.0000    ! precisely correct !

Solved.

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On radioactive decay,  see the lesson
    - Radioactive decay problems
in this site.

You will find many similar  (and different)  solved problems there.


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Also,  you have this free of charge online textbook in  ALGEBRA-I  in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic "Logarithms".


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Free of charge online textbook in ALGEBRA-I
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to your archive and use it when it is needed.